Course 11

GERTC Review Lectures

Course 11

Lecture 11-1: Stresses in Beams & Reinforced Concrete

Foundation PressureGross and Net PressuresWith upliftExamples:Rectangular footing with axial and moment loadsRectangular footing supporting a pedestalFooting subjected to column not at its centerColumn subject to axial load and momentConcrete wall centrally located on a footingConcrete retaining wallFooting subject to moments in both axesReinforced ConcreteCodes (2015 NSCP)Spacing of reinforcementExample - Rectangular beamExample - Square columnBundled barsTies and spiralsDevelopment LengthBars in tensionModification factorsBars in compressionExample - cantilever beamConcrete coverShrinkage and temperature reinforcementExampleModulus of elasticity, rapture, and modification factorImmediate deflectionExampleLoad factors and combinationMethods of AnalysisTwo spans, column endsTwo spans with spandrel beamTwo spans with simple supportThree spansExample

Lecture 11-2: Surveying

CurvesTypes of horizontal curvesSimple circular curveExampleCompound curveExample 1Example 2Example 3Reversed curveExample 1 - Reversed curved connecting parallel roadsExample 2 - Parallel roads connected by equal turnoutSpiral curvesExample

Lecture 11-3: Indeterminate Beams

Propped cantilever beamsExample 1Example 2Continuous beamExample - By superpositionDegrees of indeterminacy of frames and trussesExample - Classify each structureTrussesExamplesFramesExamplesMulti-storey rigid frameThree-moment equationFormulas for 6Aa/L and 6Ab/LExample

Lecture 11-4: Permeability

Permeability (flow of water through soils)Darcy's lawNotable formulasPermeability testsConstant head testFalling head testEquivalent hydraulic conductivitiesParallel (horizontal) flowNormal (vertical) flowPumping wellsUnconfined wellsConfined wellsExample:Constant head testConstant head test 2Falling head testFalling head test 2Flow through permeable layerEquivalent hydraulic conductivity of layered soilNormal flow through layered soilLayered soilFlow through layered soil 2Confined aquiferPumping well

Lecture 11-5: Probability & Statistics

Simple probabilityExamples:Ball drawn from a boxCard drawn from a deckRoll a pair of dice. Sum of 11Roll a pair of dice. Sum of 10 or 123 balls drawn from a bag6 books arranged in a shelf10 books arranged randomly in a shelfLottery tickets3 cards drawn randomlyPoker gameDrawing exactly 3 face cardsCompound probabilityIndependent eventsDependent eventsExamples:Probability that a man will be aliveTwo bags containing white and black balls3 cards drawn, all aces3 students are randomly chosen to get out of the roomBox with defective cell phonesBox with marblesMutually exclusive eventsProbability of getting at least 1 in two throws of diceGame of chessProbability that a problem is solvedProbability that a target is hitOne ball drawn from each of the two bagsThree candidates for an officeProbability that there are at least four face cardsBinomial distributionBox with defective cell phonesProbability that it will rainProbability that 5 of the 12 employees have at least one credit cardThrow of 9 diceProbability of getting a 9 in 3 throws of diceProbability of getting at least 2 ones...Probability that fewer than 4 will use a couponOdds of getting three heads in tossed coinsProbability to complete 4 years in college

Lecture 11-6: Forces in Space

Rectangular components of force in spaceUnit vectorUsing the VECTOR MODEExamples:Vector componentsVector components 2Resultant of forces in spaceMoment about an axisMoment about a pointExample 2Equilibrium of forces in spaceSupport reactionsTwo-force membersDoor hingesExamples:To lift a table without tilting ...Circular steel plate supported by 3 equally spaced postsTriangular plate supported by 3 vertical cablesRectangular plate suspended from 4 wiresLoad supported by tripodUsing calculator MODE MATRIXBoom supported by two cablesHomogeneous bar resting on vertical wallWindow supported by a wirePole supported by two cablesTwo bars supported by a cableMoment about a lineBoom supported by two cablesTwo bars supported by a cable

Lecture 11-7: Probability and Statistics

Probability and statistics (continuation)Binomial distribution examplesProbability that the shipment will make it throughMultinomial distribution examplesA fair dice is thrown five times...Box containing ballsA traffic engineer...Poisson distribution examplesRoad construction projectsCars approaching an intersectionDefective bulbsBad reaction from injectionDefective itemsNormal distributionExamples:Assembly lineUsing calculator MODE STATPollutants dumped into a riverDefective washersUsing calculator MODE STAT